Diff for "AmdahlsLaw"

Differences between revisions 8 and 30 (spanning 22 versions)

<<latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)>>

Notice that we are talking about the entire task here and that performance (speedup) is defined in terms of execution time! So we have to define the following:

latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$) (1)

This gives a new Execution time of

latex($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)

So we have

latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)

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-  ⇤ ← Revision 8 as of 2005-06-27 22:16:45 → 
  Size: 1579
  Editor: yakko
  Comment:
+   ← Revision 30 as of 2008-10-24 02:23:46 → ⇥
  Size: 720
  Editor: 209-142-131-35
  Comment:
-Deletions are marked like this.
+Additions are marked like this.
 Line 3:
-{{{#!latex2
\begin{equation}
   Speedup = \frac{Performance~for~entire~task~using~the~enhancement~when~possible}{Performance~for~entire~task~without~enhancement}
\end(equation}
}}}

Hello

{{{
           Performance for entire task using the enhancement when possible
Speedup = -----------------------------------------------------------------
              Performance for entire taks without using the enhancement
}}}
+<<latex($$Speedup = \frac{Performance~using~enhancement~when~possible}{Performance~without~enhancement}$$)>>
-Line 21:
+Line 9:
-{{{
                  Old Execution Time
SpeedupOverall = --------------------
                  New Execution Time
+[[latex($$SpeedupOverall = \frac{Old~Execution~Time}{New~Execution~Time}$$)]] (1)
-Line 26:
+Line 11:
-                                                                    FractionEnhanced
New Execution Time = Old Execution Time ( (1 - FractionEnhanced) + ------------------ )
                                                                    SpeedupEnhanced
+This gives a new Execution time of
-Line 30:
+Line 13:
-or

                       Execution Time affected by Improvement
New Execution Time =   --------------------------------------  + Execution Time unaffected
                            Amount of Improvement (x times)
+[[latex($$New~Exec~Time = Old~Exec~Time \left( 1 - FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}\right)$$)]]
-Line 37:
+Line 16:
-
SpeedupOverall = --------------------------------------------
                                           FractionEnhanced
                 (1 - FractionEnhanced) + ------------------ )
                                           SpeedupEnhanced
-Line 43:
+Line 17:
-}}}
+[[latex($$SpeedupOverall=\left(\frac{1}{1-FractionEnhanced + \frac{FractionEnhanced}{SpeedupEnhanced}}\right)$$)]]